Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design

Implementation theory links together social choice theory and game theory. At a less abstract level, its application provides an approach to welfare economics based on individual incentives. The underlying motivation for implementation theory is most easily seen from the point of view of a relatively uninformed planner who wishes to optimize a social welfare function that depends on environmental parameters about which relevant information is scattered around in the economy. Thus, the planner wishes to both collect as much of this relevant information as possible, and, with this information, make a social decision (e.g., an allocation of resources). This is the classic problem identified by Hurwicz (1972). In the twenty years since, we find numerous research agendas falling into the general category of implementation problems: the study of planning procedures, contracts, optimal regulation and taxation, agency relationships, agendas and committee decision-making, comparative electoral systems, non-cooperative foundations of general equilibrium theory, and even much of the recent theoretical work in accounting and the economics of law.